DAVIDB. LTJDLUM
1240
Vol. 60
MICELLE FORMATION I N SOLUTIONS OF SOME ISOMERIC DETERGENTS BY DAVIDB. LUDLUM~ Contribution f r m the Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received Febrwry 84, 1968
Measurements of electrical conductivity and of optical turbidity are reported,forsolutions of three isomeric dodecylbenaene sulfonates in water solution. The conductance behavior of these solutions is similar to that which has been reported for other detergents, while the light scattering behavior is typical of solutions of highly charged particles. Critical concentrations and micelle sizes have been determined from these measurements, and the conclusion has been drawn that an increase in hydrophobic nature lowers the critical micelle concentration and increases the micelle size in agreement with the predictions of recent theories of micelle formation.
Introduction Micelles are formed in solutions of ionic detergents when the energy gained by bringing the hydrophobic parts of the monomers together is sufficient t o overcome the opposing repulsive forces. This study was undertaken to determine the effect of varying the hydrophobic nature of an anionic detergent on the critical micelle concentration and on the properties of the micelles themselves. Three isomeric sodium dodecylbenzene sulfonates, differing from each other in the point of attachment of the benzene ring to the dodecyl chain and exhibiting a varying hydrophobic nature resulting from differences in the effective length of the hydrocarbon side chain, were chosen to investigate any such effects. Debye3 has studied a series of cationic detergents and has found that an increase in hydrocarbon chain length leads to the formation of larger micelles a t lower concentrations. Because of the importance of such studies to recent theories of micelle formation, they have been extended here to a series of anionic detergents which show similar behavior, modified somewhat by the high charge on the micelle. Dodecylbenzene sulfonates were selected because they are strong electrolytes not hydrolyzed in solution, and because they are relatively soluble. Critical micelle concentrations were determined from measurements of electrical conductivity, and micelle sizes were obtained from light scattering measurements.
Theory The theory of micelle formation has been discussed in recent articles by other Briefly, micelles are formed when the energy released by the aggregation of the hydrocarbon parts of the monomers is sufficient to overcome the electrical repulsion among the ionic groups and to balance the decrease in entropy accompanying the formation of micelles. A balance of these opposing forces leads to the formation of micelles of a defin,te size a t and above the critical micelle concentmtion. 'Theories of micelle formation express the total free energy of the system in terms of the moIec(1) This paper is based on a thesis aubrnitted by David B. Ludlurn to t h e Faculty of t h e University of Wisconsin in partial fulfillment of the requirementa for the degree of Doctor of Philosophy, August,
1954.
(2) E. I. du Pont de Nemours and Co., Polychemicals Department, Experimental Station, Wilrnington, Delaware. (3) P. Debye, Ann. N . Y. .4cad Sci., 61, 575 (1949). (4) 1 '. Ooshika, J . Colloid So.,9, 254 (1954). (5) I. Reioh, THISJ O U R N A 60, L 257 , (1956).
ular characteristics of the monomer and the micelle. Free energy is then minimized with respect to micelle size and critical concentration yielding expressions relating these two quantities to the characteristic properties of the detergent. The detergent monomer may be characterized in part by a parameter, Wn, which measures its hydrophobic nature. This parameter is related to the area of hydrocarbon exposed to water in solution and to the attractive forces which exist between the hydrocarbon parts of different monomers. The higher dependence of the electrical energy on the number of monomers in a micelle leads to the prediction that an increase in Wn, or an increase in the hydrophobic nature of the monomer, will result in an increase in micelle size and a decrease in critical concentration if all other properties of the detergent remain the same. This condition is most nearly met in isomeric detergents where only the hydrocarbon part of the monomer is varied. In order to determine values of n, the number of monomers in a micelle, and Co, the critical concentration, from experimental conductivity and light scattering measurements, it is necessary to investigate the equilibrium which exists between monomers and micelles. For the formation of a micelle containing n anions and p gegenions in an anionic detergent, we may write approximately, substituting molar concentrations for activities: CM/CA~CBP = K , where K is an equilibrium constant, CM is the concentration of the micelle AnBp-(n-P), CA is the concentration of monomer A-, and CB is the concentration of gegenion B+. Using Debye's notation, we take Co to be an arbitrary constant which is later identified with the critical micelle concentration, and set K = Cn'+p,. YM = CM/Co, YA = CA/CO,and YB = CB/CO. Finally, we introduce the quantity y = C/Co, where C is the molar concentration of anion or gegenion we would have if there were no association, and add two equations representing the conservation of mass in micelle formation. We then have the following system of equations describing the monomer-micelle equi1ib rium
p
YM
f YB
= Y
Equations 1 may be solved numerically (for particular values of n and p ) to give ?A, YB and TM as functions of y. The results of one such calculation, with n equal to 70 and p equal to 50, are shown in Fig. 1. Similar results are obtained for other values of n and p if n is sufficiently large;
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Sept., 1956
MICELLE FORMATION IN SOLUTIONS OF ISOMERIC DETERGENTS
the conclusions which follow have been verified for n greater than 20, the range of values experimentally encountered. We note from Fig. 1 that micelles first appear a t y approximately equal t o 1, or (7 = Co; this is the justification for identifying Co, defined by the equation R = CO1-n-P, with the experimentally observed critical micelle concentration. For values of y greater than one, it is also clear that YM is a nearly linear function of y with a slope, A.YM/A.Y, of 1/70. It has been established by direct calculation that A y ~ / A ymay in general be closely approximated by l/n, independent of the value of p . Thus, for n equal to 70, AYM/AY is a t most 3.8% different from l/n, where p varies from 0 to 70. Accordingly, we may to a good approximation express CM as a linear function of C C M = (C - Ca)/n (2) This equation is useful in the treatment of the light scattering data. It is not necessary to develop a detailed theory of conductivity in detergent solution to determine critical concentrations from conductivity data. If we plot specific conductance versus concentration for a detergent solution, we obtain a graph consisting of two intersecting straight lines. Below the critical concentration, the conductance increases as the concentration of detergent monomers and gegenions increases; above the critical concentration, highly charged micelles are also present, and conductance increases a t a different rate. The critical concentration may, therefore, be determined from the point a t which the slope of the specific conductance versus concentration curve changes. Ionic interactions contribute to slight deviations from linearity in each region and, in addition, make it difficult to relate micellar mobilities to the molecular characteristics of the micelles. Nevertheless, some information on the relative micelle size and charge may be obtained by comparing the conductivity data for related detergents above the critical concentration. The theory of the scattering of light from solutions of highly charged particles has been treated in a number of recent article^.^.' The equation relating amount of light scattered to the concentration of ions in solution is given by Prins and Hermans as
where n, p and CA are defined above, cz is the concentration of micelle in g./ml., M is the molecular weight of the micelle, R ~ iso Rayleigh’s ratio, and K is the scattering constant; 2 i ~ ~ n ~ ~ ( d n NXo4. Here, no is the refractive index of solvent, dn/dc2 is the change in refractive index with concentration of micelle (taken equal t o dnldc), N is Avogadro’s number and Xo is the wave length of incident light. Equation 3 may be simplified if we refer to Fig. 1 and consider CA t o be an approximately linear function of CM and hence of C2 above the critical (6) P. Doty and R. F. Steiner. J . Chum. Phrs., 90,85 (1952). (7) W.Prim and J. J. Hermans, THISJOUBNAL,59, 576 (1955).
I
1241 7% I
5- 0.20
4-
- 0.15
i.$ 3-
5
0.10
2-
0.05 t
I
0
I
I
I
I
I
I
1
1 i* - 0
8 10 12 14 16 18 Relative detergent concn., y Fig. 1.-Relative concentrations in a detergent solution: ?A, relative monomer concentration; YE, relative gegenion concentration; y y ~ ,relative micelle concentration. 2
4
6
concentration. Then, equation 3 may be written in the form KCZ - (1 R N
+
DlCZ)
=
1
+
(4)
Here, D1and D2are constants which could be evaluated in terms of n, p , Coand M . However, no precise significance has been attached to these constants here and equation 4 has been used in this form simply to guide the extrapolation of the quantity Kcn/Raoto zero concentration. If we neglect the slight difference between the molecular weight of the micelle, and n times the molecular weight of the detergent monomer and gegenion, equation 2 gives c2 in terms of the experimental quantity “c”, the total detergent concentration. Thus, c2 = c - co, where all concentrations are expressed in g./ml. From the extrapolated value of Kc2/R90, we may obtain a value for the molecular weight, M , of the micelle and thus for the aggregation number, n.
Experimental Highly purified samples of the three isomeric dodecyl benzene sulfonates studied here were supplied by Dr. D. G. Kolp, Procter and Gamble Company, Cincinnati, Ohio. These compounds were designated sodium 2-dodecylbenzene sulfonate (Na 2-DBS), sodium 3-dodecylbenzene sulfonate (Na 3-DBS) and sodium 4-dodecylbenzene sulfonate (Na 4-DBS), corres onding to the sodium salts of monosulfonated 2-phenyldo$ecsne, 3-phenyldodecane and 4phenyldodecane, respectively. According to Dr. Kolp, the position of the benzene rin on the side chain was known definitely from the method of synthesis. The compounds were carefully extracted with petroleum ether to remove unsulfonated hydrocarbon and recrystaIlized from isopropyl alcohol to remove other electrolytes. Infrared absorption data indicated, however, that some of the mdu as well &B the pum isomer may have been present; steric effects apparently prevented the formation of very much of the d h o isomer In making up solutions for conductivity and light scatterconsiderable care had to be exercised to / ing d ~measurements, )~/ obtain the true dry weights of the detergene since these compounds are hygroscopic. The dilute solutions required for conductivity measurements were made by adding conductivity water from a calibrated pipet to a known weight of dried detergent. Concentrations on a volume basis were calculated from the known weight of solution by assuming that the density was not significantly difierent from that of water; for the low concentrations used, about 0.001 molar, thie b a reasonable assumption. More concentrated solutions for light scattering studies were made up in volumetric flasks. The and Northrup equipment wed to measure. the conductivlties of the detergent solutions has been described
.
DAVIDB. LUDLUM
1242
adequately elsewhere.ssQ A water thermostat, in which the conductivity cell could be submerged, was used to control the temperature to within f0.005" a t 25" and a t 30'. The conductivity cell itself was of the vertical type and had a capacity of about 19 ml. and a cell constant of 0.834. It was used with bright platinum electrodes because detergents are strongly absorbed from solution by spongy platinum. The fact that the resistance did not change appreciably with time or frequency of signal indicates that this procedure did not introduce any error from polarization. All conductivities were determined a t 1000 cycles per second and checked occasionally a t 500 and 2000 c.p.s. Light scattering measurements were carried out in a commercial photometer manufactured by the Phoenix Precision Instrument Company, and described in a paper by Brice, Halwer and Speiser.'o This instrument was used essentially as received from the manufacturer, except that two heating elements consisting of a large number of copper fins soldered onto s/s-inch copper tubing were installed inside the photometer. By circulating water through the tubing from a large external thermostat, the temperature insi$e the instrument could be held constant to within about 1 , at temperatures between 25 and 35". The instrument came supplied with an opal glass diffuser which served as a standard to relate galvanometer readings to reduced intensity of scattered light. The accuracy of this calibration was checked by determining the reduced intensity from solutions of standard polystyrene received from Professor Debye's laboratory; for these solutions, the value of ROObased on the opal glass calibration agreed to within 1% of the accepted value. Two important experimental difficulties were encountered in determining values of R80 for detergent solutions. One of these, the removal of dust from the solutions, is common to all detergents. The other problem, fluorescence resulting from minor impurities in these particular detergents, was important only when blue incident light was used, and was avoided by employing green (546 mw) light. Although pressure filtration through an ultra-fine sintered glass filter proved to be quite an effective means of removing dust from pure water, it was soon evident from the inconsistent results obtained that it was not satisfactory for detergent solutions. Examination of solutions which had been treated in this manner indicated that fine particles of glass were being removed from the filter by the detergent. A Selas micro-porous (03 porosity) porcelain filter showed the Rame difficulty. Since the ultra-fine glass filter appeared to remove the ordinary pa1,ticles quitp well, the procedure finally adopted was to filter the solutions into dust-free centrifuge tubes and centrifuge out the heavier glass particles. For this purpose, a Model SS 1-a Serval1 centrifuge, capable of developing fields of the order of 20,000 times gravity, was employed. After 3 hours of centrifugation, 25 nil. of Folution was
5
I0 3 S
G
m
2l -J. . - , / I
0
2
Fig. 2.-Conductivity
6 8 10 c X IO', g./ml. of sodium dodecylbenzenesulfonstcs.
4
( 8 , "Direction Books No. 1296 and 11208," Leeds and Northrup Company, Philadelphia, Pa. (9) P. H. Dike, Rev. Sci. Instr., 3, 379 (1931). (10) B. A. Brice, M. Halwer and R. Syeiser, J . O p t . Sot. A m . , 40, 768 (1950).
Vol. 60
withdrawn carefully from each of two centrifuge tubes and transferred to a commercial semi-octagonal dissymmetry cell. This technique resulted in highly consistent data, an apparent lack of dust as determined by visual examination, and low values of the dissymmetry ratio. Since repeated filtration followed by centrifugation did not change the values of R N , it was apparent that neither process was affecting the concentrations of the solutions. Direct confirmation of this was obtained by checking the refractive index of a solution which had been filtered to make sure that the concentration had not changed. The other experimental quantity needed to interpret the light scattering data was a value of dnldc, the specific refractive index increment for the detergent. This quantity was measured on a differential refractometer which has been described by Dismukes and Alberty.11 Green light for measurements was isolated from an AH 4 mercury lamp with a W r a t h 77a filter, and solutions of sucrose were used for calibration. Refractive index measurements were made a t 25", but it was found that ( n m)/c is not sensitive to small variations in temperature.
-
Results Conductivity Measurements.-Data from conductivity measurements are presented in Fig., 2 where specific conductance of the solute (specific conductance of the solution minus specific conductance of the solvent) is plotted against detergent concentration. Specific conductances a t 25" are read from the vertical axis a t the right-hand side of the figure; specific conductances a t 30°, from the vertical axis a t the left-hand side of the figure. The critical concentrations determined from this graph are listed in Table I. TABLE I Detergent
Na 2-DBS Na 3-DBS Na 4-DBS
G./ml.
Critical concn. in Mole/l.
4 . 1 5 x 10-4 5 . io x 10-4 5.53 x 10-4
1.19 1.46
1.59
x 10-3 x 10-3 x 10-3
These values are for either 25 or 30"; there was 110 appreciable change of critical concentration with temperature. It is interesting to note that the conductivities of all three detergents fall on the same straight line in the monomer region: This implies that the equivalent conductance of the detergent monomer, YA-, is nearly the same for all three isomers arid that the differences in conductivity appearing in the micelle region are due to differences in the micelles themselves. It is clear from Fig. 2 that the micelles formed from Na 4-DBS are more efficient in transporting electrical charge than the micelles formed from Na 3-DBS and these micelles, in turn, are more efficient than the ones formed from Na 2-DBS. These are, however, only net results which may arise from differences in shape as well as differences in size and charge on the micelles. Further interpretation of these results must, therefore, await the development of a more detailed theory which will, in addition, take into account interionic effects between these highly charged particles. The effects of n change in temperature were studied primarily because it was difficult to control exactly the temperature a t which light scattering measurements were made. However, it appears that a small change in temperature does not have (11) E. B. Disinukes and R. A. Alberty, J . A m . Chem. Soc., 75, 809 (1963).
Sept., 1956
MICELLE FORMATION I N SOLUTIONS OF ISOMERIC DETERGENTS
much effect on the properties of the micelles. It has already been noted that the cri1,ical concentrations are not measurably different a t 25 and 30"; it is clear that the conductivities themselves do change, but this may be accounted for by the change in the viscosity of the solvent. Thns, the slope of the graph of specific conductance versus concentration in the monomer region increases I)y exactly the same factor that the solvent viscosity decreases and, within experimental error, this is also true i n the micelle region. It seems probable, therefore, that the micelles formed a t 30" are not appreciably different from those formed a t 2 5 O , a conclusion borne out by the light scattering data. Refractive Index Measurements.--The results of refractive index measurements a t 25" are given by the equation, n - no = 0 . 1 7 2 4 ~with ~ an average deviation for the experimental data of 0.8%. This equation applies only to solutions of Na 3-DBS and Na 4-DBS; the other detergent, Na 2-DBS, was too insoluble for light scattering and refractive index measurements a t these temperatures. hlthough a break in graphs of the quantity n - no versus c has been reported a t the critical micelle concentration for a number of other detergents, careful measurements with blue light carried out by the author a t the Procter and Gamble Go. Miami Valley Research Laboratories have not indicated any departure from a linear relationship for these detergents. Substituting the value, 0.1724 ~ m . ~ / gfor . , ( n - no)/cin the definit,ion of the light scattering constant, K, we obtain K = 1.951 X 10-7 mole cm.2/g.2for experiments with green light. Light Scattering Measurements.--The light scattering data for solutions of Na 3-DBS are presented in Fig. 3, and similar data for Na 4-DBS, in Fig. 4. For each of these detergents we have plotted tho usual light scattering parameter, c21 R90, (read from the left hand vertical axis) versus cz, the weight concentration of micelle. For uncharged particles, such a graph is usually a straight line and the y-intercept leads to a value for the molecular weight of the scattering unit. Here, marked curvature is evident and, although the intercept a t c2 = 0 is still proportional to the reciprocal of the molecular weight, some guide to the extrapolation is clearly ilecessary; this has been supplied by equation 4 which predicts that, for the appropriate value of DI,a graph of cq'Rsn(1 D1c2) versus c2 mould be a straight line. Actually, it was found that fair :tpproximations to straight lines were obtained for a range of values of 01,and that all of these graphs had nearly the same intercept, or value of l/Kh/. It was decided, therefore, to determine the best fitting straight litie in the sense that the following sum, taken over all the experimental points for a given detergent, would be a minimum
+
By differentiating this expression with respect to 1/KM, Dz/K and D1,and setting these derivatives equal to zero, we obtained equations for these constants in terms of certain averages of c2i and Rgoi. These equations are given in the Appendix to this paper.
0
1
2
5 G 7 8 9 10 103, g./ml. scattering from solutions of sodium 3dodecylbenxenesulfonate. 3
4
c2
Fig. 3.-Light
1243
x
l
0
I
2
Fig. 4.-Light
x
5 6 7 8 9 10 103, g./ml. scattering from solutions of sodium 4dodecylbenzenesulfonate. 3
4
cz x
Evaluation of these averages led to the following values for the constants N a 4-DBS
N a 3-DBS
1/KM DdK
Di
258 1 87 X IO6 645
622 1.68 X lo6 512
Thus, according to equation 4, a graph of c2/R90 (1 6 4 5 4 against c2 for Na 3-DBS should be a straight line with an intercept of 258 and a slope of 1.87 x 106, whereas the corresponding graph for Na 4-DBS of c2/Rgo(1 5 1 2 ~against ~) c2 should be a straight line with an intercept of 622 and a slope of 1.08 x 106. These quantities have been plotted DICZ) in Figs. 3 and 4, where values of c2/Rgo(1 are read from the vertical axis on the right hand side of each figure. It is evident that the data are fitted very well by equation 4. No further interpretation has, however, been given to the values of D 1and D2here; this expression is used simply to guide the extrap~ ~ olation of values of c ~ t o ~zeroRconcentration. The curves in Figs. 3 and 4 have been drawn through the values of c2/Rg0in agreement with these best fitting straight lines. Values of A I and n for the two detergents have been calculated from the y-intercepts, and the results are presented here in tabular form
+
+
+
Na 3-DBS N~:~-DBS
I/KM
.If
n
258 622
19 0 x 103 8 . 2 X lo8
57 24
DAVID B. LUDLUM
1244
From these data, it is a t once evident that the more hydrophobic of these detergents, Nn 3-DBS, forms larger micelles than Na 4-DBS. The large charge effects which have been noted here are probably associated with the low critical concentrations of these detergents. Detergents having higher critical concentrations, and hence higher concentrations of free electrolyte, show little or no departure from linearityI2 when c2/Rw is graphed against c2. One additional qualitative observation on the light scattering behavior of these solutions may be mentioned. By means of the thermostat installed in the photometer, it was possible bo vary the temperature a t which the light Scattering measurements were made. When a carefully prepared stock solution was sealed into a light scattering cell and values of R90 determined over a temperature range of 25 to 35", no detectable variation in scattering was observed. This seems to indicate that small changes in temperature do not affect greatly the properties of the detergent micelles. For this reason, no further attempt was made to control the exact temperature a t which light scattering measurements were performed. We have thus been able to conclude that more hydrophobic detergents tend to form larger micelles a t lower concentrations than similar, but less hydrophobic, detergents. This is in agreement with the effect of a change in W,, representing the hydrophobic nature of the detergent, indicated in the section on theory of micelle formation. It should be noted that both the change in critical concentration and the change in size of micelle with hydrophobic nature result from the higher dependence of the electrical energy of interaction on the number of units in a micelle; the conclusions are, therefore, not dependent on the detailed structure assumed for the micelle. Acknowledgment.-The author takes particular pleasure in acknowledging the generous help of Professor J. W. Williams during the course of this
Vol. 60
research. He is indebted to the Procter and Gamble Company for supplying the purified detergents he has studied, and to the Wisconsin Alumni Research Foundation a d the National Science Foundation for financial assistance. Appendix Equations for the constants l / K M , D2/K and D,
_1 KAT -
A
Dz
-
K -
A
A
Here, N is the number of measurements, and A is the determinant
( 1 2 ) H. V. Tartar and A. L. hf. Lelong, THIEJOURNAL, 69, 1185 (1 955).
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